Answer:
The answer is
[tex]y = \frac{2}{3} x + \frac{37}{3} [/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
We must first write the equation in the general form above in order to find the slope
3x + 2y = - 7
2y = - 3x - 7
Divide both sides by 2
y = - 3/2x - 7/2
Comparing with the general equation above
Slope = - 3/2
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
Slope of perpendicular line = 2/3
So the equation of the line using point (-8,7) and slope 2/3 is
[tex]y - 7 = \frac{2}{3} (x + 8) \\ y - 7 = \frac{2}{3} x + \frac{16}{3} \\ y = \frac{2}{3} x + \frac{16}{3} + 7[/tex]
We have the final answer as
[tex]y = \frac{2}{3} x + \frac{37}{3} [/tex]
Hope this helps you
